Select the option that is related to the third term in the same way as the second term is related to the first term.
\(\frac{4}{3}\) : \(\frac{65}{26}\) :: \(\frac{2}{5}\) : ?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{9}{124}\)
Compare the numerators and the denominators separately with cubes: 65 is just above \(4^3=64\) and 26 is just below \(3^3=27\).
Numerator: \(4^3+1=64+1=65\)
Denominator: \(3^3-1=27-1=26\)
So the rule is: cube the numerator and add 1, cube the denominator and subtract 1
For \(\frac{2}{5}\): \(2^3+1=8+1=9\)
\(5^3-1=125-1=124\)
So the missing term is \(\frac{9}{124}\).